The Incomplete Gamma Function Expressed as a Sum of Macdonald Functions
Copyright policy )The Incomplete Gamma Function Expressed as a Sum of Macdonald Functions
The author uses the expansion of the incomplete gamma function defined by \[ \gamma(\nu,z)=\sqrt{{2\over\pi}}\int_0^z s^{\nu-1/2} K_{1/2}(s) ds,\quad \Re \nu>0, \] in terms of the modified Bessel functions of the second kind \(K_{n+1/2}(z)\). This expansion allows to evaluate different types of integrals of interest in atomic physics.
- Portland State University United States
incomplete beta and gamma functions, Physics, cylinder functions, Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals), special transforms, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Special integral transforms (Legendre, Hilbert, etc.), applicattion of quantum theory to atomic physics, Atomic physics
incomplete beta and gamma functions, Physics, cylinder functions, Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals), special transforms, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Special integral transforms (Legendre, Hilbert, etc.), applicattion of quantum theory to atomic physics, Atomic physics
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